## Problem Statement

A bullet of mass 50 g moving with an initial velocity of 100 m/s, strikes a wooden block and comes to rest after penetrating a distance 2 cm in it.

Calculate:

(i) Initial momentum of the bullet (ii)final momentum of the bullet (iii) retardation caused by the wooden block, and (iv) resistive force exerted by the wooden block

Solution:

Mass = m=50 g = 50/1000 kg =0.05 kg

Initial velocity =u = 100 m/s

Final velocity = v= 0

Distance travelled before stopping =s= 2 cm = 0.02 m

Initial momentum = mu=0.05 X 100 kg m/s=5 kgm/s

Final momentum = mv = 0 [as v=0]

Let retardation be a.

We will use the equation, ** v^2=u^2-2as** [ – sign for retardation. The bullet finally stops, that means it had a retardation]

as v=0, the equation becomes

0 = u^2 -2 a s

=> a = u^2/(2s) = (100 X 100)/(2X0.02) = 250000 m/s^2

So Retardation is 250000 m/s^2

Resistive force applied by the block = ma = 0.05 x 250000 N= 12500 N

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